Both values are approximate, rounded to 3 decimal places.
===================================================
Explanation:
I'm assuming you meant to say 16:9 instead of 16:97
The ratio 16:9 means that the horizontal width is 16x units and the height is 9x units. They form the ratio 16x:9x which reduces to 16:9
She wants the tv to be the same size as her old one, so the new tv will also have a diagonal of 42 inches (tv sizes are measured by the length of the diagonal).
Through the pythagorean theorem, we can say
a^2+b^2 = c^2
(16x)^2 + (9x)^2 = (42)^2
256x^2 + 81x^2 = 1764
337x^2 = 1764
x^2 = 1764/337
x^2 = 5.23442136498517 approximately
x = sqrt(5.23442136498517)
x = 2.28788578495194
x = 2.288
--------
This means the dimensions would be
width = 16x = 16*2.288 = 36.608 inches
height = 9x = 9*2.288 = 20.592 inches
both are approximate
Solve a combined inequality that is a conjunction of two linear equalities.
1.) solve for n. -1<9+n<17
2.) solve for x. -2<8x-12<_36
Answer:
-10 < n < 85/4 < x ≤ 6Step-by-step explanation:
1. Subtract 9:
-10 < n < 8
__
2. Add 12, then divide by 8:
10 < 8x ≤ 48
10/8 < x ≤ 6
5/4 < x ≤ 6 . . . . . with the fraction reduced
_____
The rules of equality allow us the do these operations, provided that we do them to all parts of the compound inequality. That is, when we say "subtract 9", we mean ...
-1 -9 < 9 +n -9 < 17 -9
This simplifies to the inequality we show above:
-10 < n < 8
Merlyn had 22 magic tricks to perform. He had completed 4/5 of them when the fire alarm sounded. How many magic tricks had he performed?
Answer:
Merlyn realizo 17,6 trucos de magia
Step-by-step explanatio:
Hizo 17,6 trucos de magia porque 22 dividido 5 es igual a 4,4 entonces despues haces 22 menos 4,4 da 17,6
Alana noticed that a number like 8 = 2 (i.e. ) has exactly four factors: 1, 2, 2 , and ! 2 . What other numbers are of this form have exactly four factors? Do all the perfect cubes have exactly four factors? Is it true that all numbers that have exactly four factors are perfect cubes?
Answer:
Step-by-step explanation:
Hello,
What other numbers are of this form have exactly four factors?
[tex]8=2^3\text{ has 4 factors } 1, 2, 2^2, 2^3\\\\\text{For any prime p, }p^3\text{ has 4 factors } 1, p, p^2, p^3\\\\[/tex]
Do all the perfect cubes have exactly four factors?
[tex]\text{If p is not prime, then it is not true anymore} \\ \\\text{For instance, }8^3\text{ has more than 4 factors } 1, 2^2, 2^3, 2^4, etc..[/tex]
Is it true that all numbers that have exactly four factors are perfect cubes?
6 has 4 factors : 1, 2, 3, 6 but this is not a perfect cube.
Thank you.
We know that any number can be decomposed as a product of prime numbers.
For example:
[tex]8 = 1\cdot 2\cdot 2\cdot 2[/tex]
8 has four factors if we count the 1.
Now we need to answer some questions regarding this:
What other numbers are of this form have exactly four factors?
8 is a cube number.
Remember that all cube numbers X can be written as:
[tex]X = n\cdot n\cdot n \cdot 1[/tex]
Now, if n is prime, then we can say that X is of the form of 8 and also has 4 factors.
But let's see the case:
[tex]8\cdot 8\cdot8= 512[/tex]
512 is a perfect cube, and if we decompose it we get:
[tex]512 = 8\cdot 8\cdot 8 = (2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2)\cdot (2\cdot 2\cdot 2)\cdot 1[/tex]
So we found a perfect cube that has 10 factors.
This means that not all perfect cubes have exactly 4 factors.
Now, all numbers that have exactly four factors are perfect cubes?
This is also false, just let's create a counterexample.
[tex]1\cdot 2\cdot 3\cdot 5 = 30[/tex]
the number 30 is not a perfect cube, and we can see that it has exactly 4 factors.
If you want to learn more, you can read:
https://brainly.com/question/832797
$10.00 divided by 25
Customers of a phone company can choose between two service plans for long distance calls. The first plan has a $28 monthly fee and charges an additional
$0.09 for each minute of calls. The second plan has no monthly fee but charges $0.13 for each minute of calls. For how many minutes of calls will the costs of the two plans be equal?
Answer:
700 Minutes
Step-by-step explanation:
For this problem, we need to write an expression that represents the cost per the amount of time used for each phone plan, and set the two expressions equal to each other to find how many minutes would be needed for the costs to be equal.
For the first phone plan, we have a base $28 and additional $0.09 per minute of call. This can be expressed as:
28 + 0.09x Where x is the number of minutes used
For the second phone plan, we have a flat $0.13 per minute of call. This can be expressed as:
0.13x Where x is the number of minutes used
To find how many minutes would be used to make the cost equal, we simply set these expressions as equivalent, and solve for x.
28 + 0.09x = 0.13x
28 + 0.09x + -0.09x = 0.13x + -0.09x
28 = 0.04x
28 = (1/25)x
28 * 25 = (1/25)x * 25
28 * 25 = x
700 = x
Thus, for the cost of these phone plans to be equal, you would have to use 700 minutes per month.
Cheers.
4x — 3 = —31 Solve for x
Answer:
x = -7
Step-by-step explanation:
4x — 3 = —31
Add 3 to each side
4x — 3+3 = —31+3
4x = -28
Divide by 4
4x/4 = -28/4
x = -7
Your answer would be x=-7 or -7!
Consider the following time series: t12345 6 11 9 14 15 a. Construct a time series plot. What type of pattern exists in the data
Answer:
Kindly check explanation and attached picture
Step-by-step explanation:
Given the time-series data:
Time (x) : 1 - - 2 - - 3 - - - 4 - - - 5
Data (yt) :6 - - 11 - - 9 - - 14 - - 15
The pattern which exists within the data is a linear pattern which could be inferred through the observable decrement and Incremental change in the y values at a steady or constant rate with time. The second attachment shows the linear trend line of the data.
August 22 3months later what day would it be
The height of an object tossed upward with an initial velocity of 120 feet per second is given by the formula h = −16t2 + 120t, where h is the height in feet and t is the time in seconds. Find the time required for the object to return to its point of departure.
Answer:
7.5 seconds
Step-by-step explanation:
[tex]h = - 16 {t}^{2} + 120t \\ \because \: we \: have \: to \: find \: the \: time \: required \: \\ for \: the \: object \: to \: return to \: its \: \\ point \: of departure. \\ \therefore \: plug \: h = 0 \: in \: the \: given \: euation. \\ \therefore \: 0 = - 16 {t}^{2} + 120t \\ \therefore \:16 {t}^{2} - 120t = 0 \\ \therefore \:8t(2t - 15) = 0 \\ \therefore \:8t = 0 \: \: or \: \: (2t - 15) = 0 \\ \therefore \:t = \frac{0}{8} \: or \: t = \frac{15}{2} \\ \therefore \:t = 0 \: or \: t = 7.5 \\ \because \: t = 0 \: is \: not \: possible \\ \huge \purple{ \boxed{ \therefore \: t = 7.5 \: seconds}}[/tex]
Thus, the time required for the object to return to its point of departure is 7.5 seconds.
Use inductive reasoning to predict the most probable next number in the list. 1, 4, 9, 16, 25, ?
Answer:
36
Step-by-step explanation:
Starting with 4, 9.
9 - 4 = 5 then + 2
So forward.
Answer:
1, 4, 9, 16, 25, 36
Step-by-step explanation:
This is because as you see 1 + 3 = 4, then 4 + 5 = 9, then 9 + 7 = 16. So we see that it goes like 3 + 5 + 7 + 9 + 11 + 13 . . . That is the pattern. Hope this helps!
What’s is 2000+100.000
Answer:
2,100.000
Step-by-step explanation:
Answer:
2000+100.000=2100
Its simple just calculate it in a calculator...
Total Price: The sales tax rate is 8%. If the sales tax on a 10-speed bicycle is $12, what is the purchase price? The purchase price is $ What is the total price? The total price is $ Get Help: Video eBook Points possible: 1
Answer:
Purchase Price = $150 and Total Price = $162
Step-by-step explanation:
Purchase price = Tax Amount / Tax Percentage (as decimal)
Purchase Price = $12 / .08
Purchase Price = $150
Total Price = Purchase Price + Tax
Total Price = 150 + 12 = $162
I hope this helps!
-The Business Man
Find the intercepts for this equation. x+2y=10
Answer:
Step-by-step explanation:
y= 0
x + 2(0) = 10
x = 10
(10, 0)
x = 0
0 + 2y = 10
2y = 10
y = 5
(0,5)
A woman making $3000 per month has her salary reduced by 20% because of sluggish sales. One year later, after a dramatic improvement in sales, she is given a 30% raise over her reduced salary. Find her salary after the raise. $ per month What percent change is this from the $3000 per month? %
Answer:
4%
Step-by-step explanation:
Since she first goes down 20% you would do 3000 times 20 which is 60000 and divided by 100 which is 600 and you would subtract 600 from 3000 which is 2400 and then you would multiply that by 30 which is 72000 and then you would divide by 100 which is 720 and add that to 2400 which is 3120 and to find the percent change from 3000 to 3120 you would subtract 3120 by 3000 which is 120 and you would divide that by 3000 which is 0.04 and multiply that by 100 which is 4 so the percent change would be 4%
A triangle has sides of lengths 8, 15, and 17. Is it a right triangle? Explain.
Answer: yes
Step-by-step explanation: 8^2+15^2=17^2 =289 and 17^2=289 ... 17 is the largest number so therefore its the largest side(c) .
equation- a+b=c
Andy painted 400 square feet in 3 hours. At that rate, how many cars could they wash in 7 hours? *
Answer:
It will take 5.4 hour to paint 720 square feet
Step-by-step explanation:
The question should be like this"Andy painted 400 square feet in 3 hours. How long would it take him to paint 720 square feet?"
In 3 hours = 400 square feet is painted
1 square feet is painted in [tex]\dfrac{3}{400}\ h[/tex]
To find time to paint 720 square feet multiply the above term by 720 as follows :
[tex]720\ ft^2=\dfrac{3}{400}\times 720\ h\\\\=5.4\ h[/tex]
So, it will take 5.4 hour to paint 720 square feet.
Solve equation. What is the solution set
-4(z-2)+4=21-(z-3)
Answer:
z=-75/17
Step-by-step explanation:
Expand this equation:
-4z+8+4=-21z-63
-4z+21z=-63-8-4
17z=-75
z=-75/17
What is the area of the parallelogram shown
Please help me with the question below
Answer:
She's 12 years old! i hope this helps you!
Step-by-step explanation:
In a survey of 1,003 adults concerning complaints about restaurants, 732 complained about dirty or ill-equipped bathrooms and 381 complained about loud or distracting diners at other tables.
a. Construct a 95% confidence interval estimate for the population proportion of adults who complained about dirty or ill-equipped bathrooms )
b. Construct a 95% confidence interval estimate for the population proportion of adults who complained about loud or distracting diners at other tables.
c. How would the manager of a chain of restaurants use the results of (a) and (b)?
Answer:
a
[tex]0.716 < p < 0.744[/tex]
b
[tex]0.3498 < p < 0.4089[/tex]
c
With the result obtained from a and b the manager can be 95 % confidence that the proportion of the population that complained about dirty or ill-equipped bathrooms are within the interval obtained at a
and that
the proportion of the population that complained about loud or distracting diners at other tables are within the interval obtained at b
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 1003[/tex]
The number that complained about dirty or ill-equipped bathrooms is [tex]e = 732[/tex]
The number that complained about loud or distracting diners at other tables is [tex]q = 381[/tex]
Given that the the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = (100- 95)\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Considering question a
The sample proportion is mathematically represented as
[tex]\r p = \frac{e}{n}[/tex]
=> [tex]\r p = \frac{732}{1003}[/tex]
=> [tex]\r p = 0.73[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p (1- \r p)}{n} }[/tex]
[tex]E = 1.96* \sqrt{ \frac{ 0.73 (1- 0.73)}{1003} }[/tex]
[tex]E = 0.01402[/tex]
The 95% confidence interval is
[tex]\r p - E < p < \r p +E[/tex]
[tex]0.73 - 0.01402 < p < 0.73 + 0.01402[/tex]
[tex]0.716 < p < 0.744[/tex]
Considering question b
The sample proportion is mathematically represented as
[tex]\r p = \frac{q}{n}[/tex]
=> [tex]\r p = \frac{381}{1003}[/tex]
=> [tex]\r p = 0.3799[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{ \r p (1- \r p)}{n} }[/tex]
[tex]E = 1.96* \sqrt{ \frac{ 0.3799 (1- 0.3799)}{1003} }[/tex]
[tex]E = 0.0300[/tex]
The 95% confidence interval is
[tex]\r p - E < p < \r p +E[/tex]
[tex]0.3798 - 0.0300 < p < 0.3798 + 0.0300[/tex]
[tex]0.3498 < p < 0.4089[/tex]
iff(x) = (x - 3)2
for x = 3, then f-1(x) = ?
A
VX-3
B.
√x+3
O
a VX-3
IN x + 3
Answer:
Option B. √x + 3
Step-by-step explanation:
f(x) = (x - 3)²
We can obtain the inverse f¯¹(x) of the above expression as follow:
f(x) = (x - 3)²
Replace f(x) with
f(x) = (x - 3)²
y = (x - 3)²
Next, interchange x and y
y = (x - 3)²
x = (y - 3)²
Make y the subject
x = (y - 3)²
Take the square root of both side
√x = y - 3
Add 3 to both side
√x + 3 = y - 3 +3
√x + 3 = y
y = √x + 3
Finally, replace y with f¯¹(x)
y = √x + 3
f¯¹(x) = √x + 3
The number 0.2 can be written as 2/10, so is it a rational number?
Answer:
yes it is
Step-by-step explanation:
Hope this helps✨
The Tigers had twice as many hits as the yanks.Let x= number of hits by yanks.Then ?= number of hits by tigers
Answer:
2x
Step-by-step explanation:
Since the tigers hit 2 times the number of x you would get that the tigers hit 2 times x or 2x balls
Answer:
2x.
hope it helps u...
plz mark as brainliest...
2. Metcalf School has two third-grade rooms (A and B) and two fourth-grade rooms
(C and D). Together, rooms C and D have 46 students. Room A has 6 more students
than room D. Room B has 2 fewer students than room C. Room D has 22 students.
How many students are there altogether in rooms A and B?
Answer: 50 students
Step-by-step explanation: Room D has 22 students, so room A has 28 (22+6). If room D has 22 students, then room C has 24 students (46-22). Room B has 22 students (26-2). In total, rooms A and B will have 50 students (28+22)
Simplify using like terms
1.7 + 8.23 -3.4 +4.7j
Step-by-step explanation:
Let's look at our expression:
[tex]1.7+8.23-3.4+4.7j[/tex]
The numbers without a variable at the end are like terms here. Let's add them up.
[tex]1.7+8.23=9.93\\9.93-3.4=6.53[/tex]
Then, let's add our answer, 6.53, to the term with a variable, 4.7j.
Our final answer: 6.53 + 4.7j
I hope this helps you!
Which number sentence shows the correct placement of the decimal point in the product based on the two factors A: 3.48 x 42.37 = 147.4476 B: 23.2 x 8.8 = 20.416 C: 0.39 x 7.2 = 28.08 D: 43.72 x 9.2 = 4,022.24 I NEED ANSWERS ASAP
Answer:
A
Step-by-step explanation:
Add the number of decimal places of the two numbers being multiplied to know the number of decimal places of the product.
A: 3.48 x 42.37 = 147.4476
2 decimal places + 2 decimal places = 4 decimal places
Only choice A is correct.
X+1/6=-3/5 solve
for x
Answer:
-13/30
Step-by-step explanation:
take 1/6 to other side,
x=-3/5 -1/6
taking LCM of denominators,
-8-5/30
=-13/30
Answer:
X=23/30
Step-by-step explanation:
X + 1/6 = -3/5
X + 5/30 = -18/30
-5/30 -5/30
X = -23/30
I feel like i did something wrong... but im pretty sure its right. Let me know if it's right! Hope it helps.
Solve the following linear equation. If a x is a fraction write as follows
-4/5
-6x+3=-21
X =
Answer:
x-5
Step-by-step explanation:
x=5
cause of the negt 6x and posstive 3 =21 so yeah that it for now so go for it head froce
100 points, will mark brainliest!!!! Explain why (4, 1) is not a solution to the equation y = 3x + 1.
Because if you substitute x = 4 and y = 1 in the equation of y = 3x + 1, you'll see that both sides are different.
So if we substitute x = 4 and y = 1 in the equation, we get:
1 = 3(4)+1
1 = 12+1
1 = 13
The equation isn't true though. Also we can explain why (4,1) isn't the solution to the equation by graph (you can go draw the graph of y = 3x + 1 and notice that the line doesn't pass through (4,1) )
Also how about another example? But this time, we use (0,1) which is the solution of y = 3x + 1.
Substitute x = 0 and y = 1 in the equation as we get:
1 = 3(0)+1
1 = 0 + 1
1 = 1
Since the equation is true, that means the (0,1) is one of the solution of y = 3x + 1.
Maybe, you want another example again? How about (1,4) which is also one of the solution of y = 3x + 1.
Again, substitute x = 1 and y = 4.
4 = 3(1)+1
4 = 3+1
4 = 4
Since the equation is true. Therefore (1,4) is also one of the solution of y = 3x + 1.
Also here's why (4,1) is not the solution of y = 3x + 1
Basically, from (x,y), 4 is the x and 1 is the y. If we substitute "x" in any equations, we get the "y". Meaning that the x value can be meant as "input" and we get the output "y" like Function which is it.
If we substitute x = 4 in the equation...
y = 3(4)+1
y = 12+1
y = 13
Meaning that the actual y value is 13, not 1. This explains why (4,1) isn't the right solution.
Maybe, what if we substitute y instead? Well that works. Now let's try substitute both y = 1 and y = 13 to see which is the right value.
(1) For y = 1,
1 = 3x+1
1-1=3x
0=3x
x=0 (Therefore, x = 0 and y = 1)
So the actual order is (0,1).
(2) For y = 13
13 = 3x+1
13-1 = 3x
3x = 12
x = 4 (Therefore, x = 4 and y = 13)
so the actual order for (2) is (4,13).
Basically, (4,1) is false for y = 3x + 1.
Answer:
See below
Step-by-step explanation:
Given the point (4,1) means
(x,y) = (4,1)
So, x = 4 , y = 1
Given the equation y = 3x+1
Put x = 4 and y = 1
=> 1 = 3(4)+1
=> 1 = 12 + 1
=> 1 ≠ 13
Since Left hand side doesn't equal right hand side, (4,1) is not the solution to y = 3x+1
Solve the rational expression 9x+3/12x+4
Answer:
The answer is
[tex] \frac{3}{4} [/tex]Step-by-step explanation:
[tex] \frac{9x + 3}{12x + 4} [/tex]
To solve the rational expression factorize both the numerator and the denominator.
For the numerator
9x + 3
Factorize 3 out
We have
3( 3x + 1)
For the denominator
12x + 4
Factorize 4 out
That's
4( 3x + 1)
So we now have
[tex] \frac{3(3x + 1)}{4(3x + 1)} [/tex]Reduce the expression with (3x + 1)
We have the final answer as
[tex] \frac{3}{4} [/tex]Hope this helps you